1 July 1990 Improved differentiating filter function for computing line spread functions in MTF calculations
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Abstract
MTF computations based on a "knife edge" scan, which is a numerical representation of the so-called edge spread function (ESF), require computation of the derivative of this function, thus yielding the line spread function ([SF) whose Fourier transform (FT) is the MTF. Since direct numerical differentiation is often inaccurate, the differentiation is usually accomplished by convolution with the derivative of a filter function, typically the derivative of the sinc function, sin(nfχ)/nfχ. But, since the sinc function is itself the FT of a rectangular filter, the subsequent FT of the [SF obtained by this procedure behaves as if the LSF had been abruptly truncated (set equal to zero) at the cutoff frequency, f, so that the resulting LSF is often subject to rapid oscillations (ringing). A new filter function based on the FT of a more gradually decreasing Hann function has been derived in closed form. Convolutions with the derivative of the new function yield smooth, non-oscillating LSF's. Examples of theoretical and experimental LSF's obtained by this method are presented and the qualitative limits within which this procedure is applicable are discussed.
© (1990) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Jacob Beutel, Jacob Beutel, } "Improved differentiating filter function for computing line spread functions in MTF calculations", Proc. SPIE 1231, Medical Imaging IV: Image Formation, (1 July 1990); doi: 10.1117/12.18834; https://doi.org/10.1117/12.18834
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